Max Engelstein, of the University of Minnesota-Twin Cities, presents an Institute for Advanced Study seminar on the supercooled Stefan problem, the mathematical model for how water cooled below freezing turns to ice. He explains why this freezing process can produce spontaneous nucleation and fractal-like ice patterns, unlike the melting problem, where the ice boundary stays smooth almost everywhere, a contrast recently proven rigorously by Figalli, Ros Oton and Serra. Engelstein then presents joint work with Inwon Kim and Sebastian Munoz, both of UCLA, analyzing a subclass of solutions linked to a parabolic obstacle-type problem. For this subclass, the team shows that nucleation can indeed occur but that the set of singular points cannot be arbitrarily pathological, giving concrete bounds on its size. The talk is aimed at an audience familiar with partial differential equations and free boundary problems, walking through the analytic techniques behind these bounds.